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A linear-time algorithm for computing the Voronoi diagram of a convex polygon. (English) Zbl 0696.68045
The main result of the paper is a linear-time algorithm for the problem of constructing the convex hull of a set of n points in three dimensions whose projections on the xy plane form the (counterclockwise ordered) set of vertices of a convex polygon.
As consequences, linear time algorithms are obtained for computing the Voronoi diagram and the furthest-point Voronoi diagram for a convex polyon vertex set, for updating the Voronoi diagram after deletion of a point site, for constructing the medial axis of a convex polygon, for finding the largest inscribed circle and the largest empty circle centered inside a convex polygon. These results are also used to obtain better time bounds for some algorithms for proximity-related problems. Some open problems are posed.
Reviewer: N.Korneenko

68Q25 Analysis of algorithms and problem complexity
68U99 Computing methodologies and applications
52A10 Convex sets in \(2\) dimensions (including convex curves)
52A15 Convex sets in \(3\) dimensions (including convex surfaces)
Full Text: DOI EuDML
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